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# A Theoretical Calculation of the Cosmological Constant Based on a Mechanical Model of Vacuum

Version 1
: Received: 21 December 2019 / Approved: 21 December 2019 / Online: 21 December 2019 (12:31:05 CET)

Version 2 : Received: 26 January 2021 / Approved: 29 January 2021 / Online: 29 January 2021 (15:28:06 CET)

Version 2 : Received: 26 January 2021 / Approved: 29 January 2021 / Online: 29 January 2021 (15:28:06 CET)

How to cite:
Wang, X. A Theoretical Calculation of the Cosmological Constant Based on a Mechanical Model of Vacuum. *Preprints* **2019**, 2019120287 (doi: 10.20944/preprints201912.0287.v2).
Wang, X. A Theoretical Calculation of the Cosmological Constant Based on a Mechanical Model of Vacuum. Preprints 2019, 2019120287 (doi: 10.20944/preprints201912.0287.v2).

## Abstract

We suppose that vacuum is filled with a kind of continuously distributed matter, which may be called the $\Omega(1)$ substratum, or the electromagnetic aether. Lord Kelvin believes that the electromagnetic aether must also generate gravity. We also suppose that vacuum is filled with another kind of continuously distributed substance, which may be called the $\Omega(2)$ substratum. Based on a theorem of V. Fock on the mass tensor of a fluid, the contravariant energy-momentum tensors of the $\Omega(1)$ and $\Omega(2)$ substratums are established. Quasi-static solutions of the gravitational field equations in vacuum are obtained. Based on an assumption, relationships between the contravariant energy-momentum tensor of the $\Omega(1)$ and $\Omega(2)$ substratums and the contravariant metric tensor are obtained. Thus, the cosmological constant is calculated theoretically. The $\Omega(1)$ and $\Omega(2)$ substratums may be a possible candidate of the dark energy. The zero-point energy of electromagnetic fields will not appear as a source term in the Einstein's equations. The cosmological constant problem is one of the puzzles in physics. Some people believed that all kinds of energies should appear as source terms in the Einstein's equations. It may be this belief that leads to the cosmological constant problem. The mass density of the $\Omega(1)$ and $\Omega(2)$ substratums is equivalent to that $31.33195$ protons contained in a box with a volume of $1.0 {m}^{3}$.

## Subject Areas

cosmological constant; dark energy; general relativity; electromagnetic aether; vacuum mechanics.

Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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